Welcome to the area!
I’d suggest taking a look at places like Chesterfield, Mechanicsville, Hanover County for property. Depending on how far you are willing to drive, I personally like Caroline County and it is also a bit cheaper.
Our local dressage chapter (I actually live further north but have been a member of this organization) is VADACC (http://vadacc.org). You make take a look on there to get a feel of the surrounding areas.
In terms of trainers, Lani Tigchelaar is in Hanover and just wonderful. Cannot say enough good things about her and if you search these forums for trainers in the area, her name comes up many times. Very effective and best teaching style I’ve experienced. Before living in [sort of] Central VA, she use to travel at the boarding barn I was at in NoVA about ten years ago. I worked with her as an event rider and she made the biggest impact on my very complicated, strangely built QH/Standardbred. Livesaver! Once I moved, I actually ended up switching to dressage but worked with a different (and also wonderful) trainer. At one point though, I decided I needed a change and found Lani again since she was pretty close to me. Man! I’ll just say she made all the difference in not just my scores (about a 6% boost pretty much immediately) but made everything super simple and gave me some very effective exercises. Can’t say enough good things.
Since you posted on the eventing thread, you also have Laine Ashker in the Richmond area too. She rides pure dressage as well and though I haven’t ridden with her, I’m sure she would be great.
There are also a lot of fantastic clinicians that come through the area as well.
Can’t really speak about farriers in that area but as for vets you have Woodside Equine Clinic close by. I personally use a smaller, “one man” clinic who I can recommend to you depending on where you end up living.
Let me know if I can help you with anything else!